In an earlier post we had
shared how easy it was for Abhi to learn to write Hindi. We later realized that
that story (and other stories of our children learning) could be read in a way completely different than intended by us. It
could be read as a story of an exceptional child, doing something exceptional.
Instead, our intention was to illustrate how easy it is for any child to
learn to write, provided the child is motivated and the methodology sensible.
This post continues in the same vein and we hope it will not be read in as a
story of exceptionalism.
Aparna has always been fascinated with
numbers and basic arithmetic, as we wrote earlier. Recently
we were surprised when she demonstrated some sophisticated mathematical
thinking that was not ever taught.
We occasionally go see Dev’s
sister in a different part of Chennai and the bus ride is typically long. During
one of these rides, Aparna wanted to do division that involved “big” numbers. So I
asked her what 39 divided by 3 was. After working on it for a minute, she came up with the correct answer and was
eager to share her algorithm with me. Here is the translated version of it:
“Let us set aside 9 and consider
only the number 30 for now. So the question becomes ‘what is 30 divided by 3?’
30 is a big number for me. So I am going to halve it and the question now is
‘what is 15 divided by 3?’ I know that there five 3’s in 15. Now I go back and use
this information to answer the previous question – i.e. 30 divided by 3 must be
twice as much as 15 divided by 3, which leaves me with the answer 10. Now I bring
back the 9 which was left out earlier. I know that there are three 3’s in 9. So
I add 3 to 10 and that is it!”
Weeks later I realized that what Aparna described to me, incidentally, is a problem solving strategy called “Decomposing and Recombining” by G. Polya in his famous work How to Solve It.
I believe that the enormous amount of time and freedom with which she has explored numbers on her own has helped Aparna build the number sense that is depicted here.
-- Hema
